Subgroups — #37548871

Order 23168.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₈₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#26042205	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₁₈₁	C₂	1	1	yes	maximal, characteristic
4	#19153885	—	2	1	no	—
5	#19153866	—	2	1	no	—
6	Q₁₆×D₁₈₁	—	2	1	no	—
7	Dic₁₄₄₈	C₄	1	1	yes	characteristic, complemented
8	#19153762	—	2	1	no	—
9	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
10	Q₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#10624382	—	4	1	no	—
12	Q₈×D₁₈₁	—	4	1	no	—
13	Dic₇₂₄	—	2	1	no	—
14	#15668439	—	4	1	no	—
15	C₈×D₁₈₁	D₄	1	1	yes	characteristic
16	#15668424	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₈₁	—	2	1	no	—
18	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
19	C₂×#10624382	—	8	1	no	—
20	Dic₃₆₂	—	4	1	no	—
21	Dic₃₆₂	—	8	1	no	—
22	C₄×D₁₈₁	—	8	1	no	—
23	C₄×D₁₈₁	D₈	1	1	yes	characteristic
24	#13089678	SD₁₆	1	1	yes	characteristic
25	Q₈×C₁₈₁	—	4	1	no	—
26	C₈×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×D₁₈₁	D₁₆	1	1	yes	characteristic
28	#10624382	—	16	1	no	—
29	C₄×C₁₈₁	—	8	1	no	—
30	C₄×C₁₈₁	#102	1	1	yes	characteristic
31	Dic₁₈₁	—	8	1	no	—
32	Dic₁₈₁	SD₃₂	1	1	yes	characteristic
33	C₂×C₁₈₁	#357	1	1	yes	characteristic
34	D₁₈₁	SD₆₄	1	1	yes	characteristic
35	D₁₈₁	Q₆₄	1	1	yes	characteristic
36	C₁₈₁	#1416	1	1	yes	characteristic, complemented, Sylow
37	#1416	—	181	1	no	maximal, Sylow
38	C₂×Q₃₂	—	181	1	no	—
39	C₂×C₃₂	—	181	1	no	—
40	#366	—	181	1	no	—
41	C₂×Q₁₆	—	362	1	no	—
42	Q₃₂	—	362	1	no	—
43	Q₃₂	—	181	1	no	—
44	Q₃₂	#10624382	1	1	yes	characteristic, complemented
45	C₂×C₁₆	—	181	1	no	—
46	#107	—	362	1	no	—
47	C₃₂	—	362	1	no	—
48	C₂×Q₈	—	724	1	no	—
49	Q₁₆	—	2	1	no	—
50	Q₁₆	—	362	1	no	—
51	Q₁₆	—	724	1	no	—
52	C₂×C₈	—	181	1	no	—
53	C₄⋊C₄	—	724	1	no	—
54	C₁₆	—	181	1	no	—
55	C₁₆	C₂×#10624382	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	Q₈	—	1448	1	no	—
58	Q₈	—	724	1	no	—
59	C₂×C₄	—	1448	1	no	—
60	C₂×C₄	—	1448	1	no	—
61	C₂×C₄	—	181	1	no	—
62	C₈	—	181	1	no	—
63	C₈	C₂²⋊#10624382	1	1	yes	characteristic
64	C₂²	—	181	1	no	—
65	C₄	—	8	1	no	—
66	C₄	—	2896	1	no	—
67	C₄	—	1448	1	no	—
68	C₄	—	181	1	no	—
69	C₄	#19153878	1	1	yes	characteristic
70	C₂	—	181	1	no	—
71	C₂	—	181	1	no	—
72	C₂	#26042191	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26042191
commutator	C₁₆×C₁₈₁	C₂×C₄
Frattini	C₁₆	C₂×#10624382
Fitting	Q₃₂×C₁₈₁	C₄
socle	C₂×C₁₈₁	#357
prime radical	C₂×D₁₈₁	D₁₆
cosocle	C₁₆×D₁₈₁	C₂²
hypercenter	Q₃₂	#10624382
hypocenter	C₁₈₁	#1416
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. Dic₁₄₄₈	C₄	semidirect
10. Q₃₂×C₁₈₁	C₄	semidirect
36. C₁₈₁	#1416	semidirect
44. Q₃₂	#10624382	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₈₁⋊C₃₂	2
#26042205	2
Q₃₂×D₁₈₁	2
#1416	181